Intermediate Algebra for College Students (7th Edition)

by
Blitzer, Robert F.

Published by
Pearson

ISBN 10:
0-13417-894-7

ISBN 13:
978-0-13417-894-3

Chapter 9 - Mid-Chapter Check Point: 24

Answer

evaluation is not possible

Work Step by Step

Note that $8=2^3$. Thus, the given expression is equivalent to:
$=\log_3{(\log_2{(\frac{1}{2^3})})}$
Use the rule $\dfrac{1}{a^m} = a^{-m}$ to obtain:
$=\log_3{(\log_2{(2^{-3})})}$
RECALL:
$\log_b{b^x} = x$
Use the rule above to obtain:
$=\log_3{(-3)}$
Note that the logarithmic function is defined as:
$y=\log_b{x} \longrightarrow b^y=x$ where $x \gt 0$
The expression above has $x=-3$.
Since logarithms are only defined when $x \gt 0$, then the given expression cannot be evaluated.